Sorry to be so harsh, but the specific experiment reported here is of little to none value outside of science. Why?
Hysteretic resistive switching in metal oxide systems is a well known phenomenon (RRAM) and occurs in all transition metal oxides with noble eletrodes. This is what has been recristened as "Memrestor" by HP. It is widely agreed upon that this switching mechanism is due to a redox reaction where oxygen is added or removed from the insulator. The specifics (filament, interfacial barrier lowering etc.) are still subject of current research though.
The experiment in the paper takes a slightly different approach: vanadium oxide has a very interesting property where its resistance switches apruptly by orders of magnitude at a certain temperature due to a reorganisation of its electronic structure. This phenomenon is known as metal to insulator (MTI) transition and has been research for at least 50 years.
The MTI has a hysteretic behavior which means that it retains its state if you vary the temperature only a little above or below the critical MTI temperature Tc. The researchers have now shown that if you keep the temperature of the system close to Tc, you can use an additional electric current to switch the resistivity of the system. A possible explanation could be self heating.
Why is it useless for practical application?
1) The phenomenon instrinsically only works at a certain temperature. Deviations by fractions of degrees K will destroy all information.
2) As far as I can see they only demonstrated electrical switching into one direction. To erase the memory both would be required.
All in all a nice experiment, but again with typical university style hype, piggybacking on the Memristor craze.
I am also relatively certain that current driven MTI switching has been reported before. I am aware of a couple of experiments where a field switched MTI transition was proposed for transistors. Those devices should exhibit exactly the same hysteresis and "memory" properties.